Witaj :)
Definicja logarytmu:
[tex]\large \boxed{\log_ab=c\iff a^c=b,\ gdzie:\ a>0\ \ \wedge \ \ a\neq 0\ \ \wedge\ \ b>0}[/tex]
[tex]a)\ \log_33=1, \ bo\ 3^1=3\\\\b)\ \log_381=4, \ bo\ 3^4=81\\\\c)\ \log_3\sqrt{3}=\frac{1}{2}, \ bo\ 3^{\frac{1}{2}}=\sqrt{3} \\\\d)\ \log _327=3, \ bo\ 3^3=27\\\\e)\ \log_3\frac{1}{9}=-2,\ bo\ 3^{-2}=\frac{1}{3^2} =\frac{1}{9} \\\\f)\ \log_3\sqrt[4]{3} =\frac{1}{4}, \ bo\ 3^{\frac{1}{4}}=\sqrt[4]{3}[/tex]
Zastosowane wzory na potęgi:
[tex]a^{-n}=\frac{1}{a^n} \\\\a^{\frac{1}{m}}=\sqrt[m]{a}[/tex]
